基于结构方程模型的多层调节效应

使用多层线性模型进行调节效应分析在社科领域已常有应用。尽管多层线性模型区分了层1自变量的组间和组内效应、实现了多层调节效应的分解, 仍然存在抽样误差和测量误差。建议在多层结构方程模型框架下, 设置潜变量和多指标来有效校正抽样误差和测量误差。在介绍多层调节SEM分析的随机系数预测法和潜调节结构方程法后, 总结出一套多层调节的SEM分析流程, 通过一个例子来演示如何用Mplus软件进行多层调节SEM分析。随后评述了多层调节效应分析方法在国内心理学的应用现状, 并展望了多层结构方程和多层调节研究的拓展方向。     

基于多层结构方程模型的情境效应分析—— 兼与多层线性模型比较

多层(嵌套)数据的变量关系研究, 必须借助多层模型来实现。两层模型中, 层一自变量Xij按组均值中心化, 并将组均值 置于层2截距方程式中, 可将Xij对因变量Yij的效应分解为组间和组内部分, 二者之差被称为情境效应, 称为情境变量。多层结构方程模型(MSEM)将多层线性模型(MLM)和结构方程模型(SEM)相结合, 通过设置潜变量和多指标的方法校正了MLM在情境效应分析中出现的抽样误差和测量误差, 同时解决了数据的多层(嵌套)结构和潜变量的估计问题。除了分析原理的说明, 还以班级平均竞争氛围对学生竞争表现的情境效应为例进行分析方法的示范, 并比较MSEM和MLM的异同, 随后展望了MSEM情境效应模型、情境效应无偏估计方法和情境变量研究的拓展方向。     

有调节的多层中介效应分析

多层中介和多层调节效应分析在社科领域已常有应用,但如果将多层中介和调节整合在一起,可以产生2（多层中介类型）×2（调节变量的层次）×3（调节的中介路径）共12种有调节的多层中介模型。面对有调节的多层中介效应分析,研究者往往束手无策。详述了基于多层线性模型的12种有调节的多层中介的分析方法和基于多层结构方程模型的4类有调节的多层中介分析方法,包括正交分割法,随机系数预测法,潜调节结构方程法和贝叶斯合理值法。这四类方法的核心议题在于如何处理潜调节项。当样本量足够大时,建议选择潜调节结构方程法;当样本量不足时,建议选择贝叶斯合理值法。随后用一个实际例子演示如何进行有调节的多层中介效应分析并有相应的Mplus程序。最后展望了有调节的多层中介效应分析研究的拓展方向。     

基于阶层线性理论的多层级中介效应

本文介绍了三种常见的多层级中介效应模型, 并根据阶层线性理论和依次检验回归系数的方法, 详述了多层级中介效应的检验步骤以及中介效应量的估计方法, 在2-1-1和1-1-1中介效应模型中, 推荐采用对层1自变量按组均值中心化, 同时将组均值置于层2截距方程式的中心化方法, 以实现组间和组内中介效应的有效分离。本文还展望了多层级中介效应模型的拓展方向, 即多层级调节性中介模型和多层级结构方程模型; 以及检验方法的拓展, 即Sobel检验和置信区间检验。     

基于结构方程模型的有调节的中介效应分析

有调节的中介模型是中介过程受到调节变量影响的模型。指出了目前有调节的中介效应分析普遍存在的问题：当前有调节的中介效应检验大多使用多元线性回归分析,忽略了测量误差;而基于结构方程模型(SEM)的有调节的中介效应分析需要产生乘积指标,又会面临乘积指标生成和乘积项非正态分布的问题。在简介潜调节结构方程(LMS)方法后,建议使用LMS方法得到偏差校正的bootstrap置信区间来进行基于SEM的有调节的中介效应分析。总结出一个有调节的中介SEM分析流程,并有示例和相应的Mplus程序。文末展望了LMS和有调节的中介模型的发展方向。     

纵向数据的中介效应分析

目前中介效应检验主要是基于截面数据,但许多时候截面数据的中介分析不适合进行因果推断,因而需要收集历时性的纵向数据,进行纵向数据的中介分析。评介了基于交叉滞后面板模型、多层线性模型和潜变量增长模型的纵向数据的中介分析方法及其四个发展。第一,中介效应随时间变化,如连续时间模型、多层时变系数模型。第二,中介效应随个体变化,如随机效应的交叉滞后面板模型和多层自回归模型。第三,中介模型的整合,如交叉滞后面板模型与多层线性模型整合为多层自回归模型。第四,中介检验方法的发展,建议使用Monte Carlo、Bootstrap和贝叶斯法进行纵向数据的中介分析。总结出一个纵向数据的中介分析流程并给出相应的Mplus程序。随后展望了纵向数据的中介分析的拓展方向。     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

中学生考试活动绩效影响因素模型的初步研究

对573名中学生进行调查研究。根据路径分析结果建立初始模型．通过竞争模型的比较,建立了中学生考试活动绩效影响因素结构方程模型：家庭因素和考试心理素质对考试活动绩效有直接效应,而学校因素、自身因素和考试心理问题与考试活动绩效之间存在间接效应;学校因素、自身因素和考试心理问题互为中介分别通过家庭因素和考试心理素质对考试活动绩效产生间接影响;考试心理素质和家庭因素互为中介对考试活动绩效产生影响。通过对超水平发挥组和发挥失常组进行比较发现,不同组之间的结构方程模型具有一致性,但是变量间的路径系数有所不同。     

纵向数据的调节效应分析

目前调节效应检验主要是基于截面数据, 本文讨论纵向(追踪)数据的调节效应分析。如果自变量X和因变量Y有纵向数据, 调节效应可分为三类：调节变量Z不随时间变化、Z随时间变化、调节变量从自变量或因变量中产生。评介了基于多层模型、多层结构方程模型、交叉滞后模型和潜变量增长模型的纵向数据的多种调节效应分析方法。调节效应的分解和潜调节结构方程法的使用是纵向数据的调节效应分析的两大特点。对基于四类模型的调节效应分析方法进行综合比较后, 总结出一个纵向数据的调节效应分析流程。随后用实际例子演示如何进行纵向数据的调节效应分析, 并给出相应的Mplus程序。随后展望了纵向数据的调节效应分析的拓展方向, 例如基于动态结构方程模型的密集追踪数据的调节效应分析。     

国内中介效应的方法学研究

中介效应可以分析自变量对因变量的影响过程和作用机制, 已成为分析多个变量之间关系的一种重要统计方法。最近20年, 中介效应成了研究方法的一个热点。从中介效应的检验方法、效应量、类别变量的中介效应检验、纵向数据的中介效应检验和模型拓展(包括多重中介、多层中介、有调节的中介和有中介的调节模型)五个方面系统总结了国内中介效应的方法学研究的发展历程。最后对中介效应的国外方法学研究进展和中介效应的未来研究方向做了讨论和拓展。     

Multilevel SEM Strategies for Evaluating Mediation in Three-Level Data

Strategies for modeling mediation effects in multilevel data have proliferated over the past decade, keeping pace with the demands of applied research. Approaches for testing mediation hypotheses with 2-level clustered data were first proposed using multilevel modeling (MLM) and subsequently using multilevel structural equation modeling (MSEM) to overcome several limitations of MLM. Because 3-level clustered data are becoming increasingly common, it is necessary to develop methods to assess mediation in such data. Whereas MLM easily accommodates 3-level data, MSEM does not. However, it is possible to specify and estimate some 3-level mediation models using both single- and multilevel SEM. Three new alternative approaches are proposed for fitting 3-level mediation models using single- and multilevel SEM, and each method is demonstrated with simulated data. Discussion focuses on the advantages and disadvantages of these approaches as well as directions for future research.     

A Comparison of Multilevel Mediation Modeling Methods: Recommendations for Applied Researchers

Multilevel structural equation modeling (MSEM) has been proposed as a valuable tool for estimating mediation in multilevel data and has known advantages over traditional multilevel modeling, including conflated and unconflated techniques (CMM & UMM). Recent methodological research has focused on comparing the three methods for 2-1-1 designs, but in regards to 1-1-1 mediation designs, there are significant gaps in the published literature that prevent applied researchers from making educated decisions regarding which model to employ in their own specific research design. A Monte Carlo study was performed to compare MSEM, UMM, and CMM on relative bias, confidence interval coverage, Type I Error, and power in a 1-1-1 model with random slopes under varying data conditions. Recommendations for applied researchers are discussed and an empirical example provides context for the three methods.     

多水平随机中介效应估计及其比较

本文在综述各类多水平中介模型的基础上, 聚焦于自变量、中介变量、因变量都来自多水平结构中较低水平的多水平随机中介效应模型, 通过蒙特卡洛模拟研究比较该模型与简化的多水平固定中介效应模型、传统中介效应模型的差别, 并考察了目前用于多水平随机中介效应的三种参数估计方法：限制性极大似然、极大似然、最小方差二次无偏估计在不同情况下对随机中介效应估计的优劣。研究结果显示：当数据符合多水平随机中介效应模型时, 使用简化模型将错误估计中介效应及其标准误, 得到不正确的统计检验结果; 使用多水平随机中介效应模型能够实现对中介效应的正确估计和检验, 其中限制性极大似然或极大似然估计方法优于最小方差二次无偏估计方法。     

A Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models

Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multilevel factor models. A brief outline of the state space formulation is provided and then state space forms for univariate and multivariate multilevel regression models, and a multilevel confirmatory factor model, are illustrated. The utility of the state space approach is demonstrated with either a simulated or real example for each multilevel model. It is concluded that the results from the state space approach are essentially identical to those from specialized multilevel regression modeling and structural equation modeling software. More importantly, the state space approach offers researchers a computationally more efficient alternative to fit multilevel regression models with a large number of Level 1 units within each Level 2 unit or a large number of observations on each subject in a longitudinal study.     

Doubly-Latent Models of School Contextual Effects: Integrating Multilevel and Structural Equation Approaches to Control Measurement and Sampling Error

This article is a methodological-substantive synergy. Methodologically, we demonstrate latent-variable contextual models that integrate structural equation models (with multiple indicators) and multilevel models. These models simultaneously control for and unconfound measurement error due to sampling of items at the individual (L1) and group (L2) levels and sampling error due the sampling of persons in the aggregation of L1 characteristics to form L2 constructs. We consider a set of models that are latent or manifest in relation to sampling items (measurement error) and sampling of persons (sampling error) and discuss when different models might be most useful. We demonstrate the flexibility of these 4 core models by extending them to include random slopes, latent (single-level or cross-level) interactions, and latent quadratic effects.

Substantively we use these models to test the big-fish-little-pond effect (BFLPE), showing that individual student levels of academic self-concept (L1-ASC) are positively associated with individual level achievement (L1-ACH) and negatively associated with school-average achievement (L2-ACH)—a finding with important policy implications for the way schools are structured. Extending tests of the BFLPE in new directions, we show that the nonlinear effects of the L1-ACH (a latent quadratic effect) and the interaction between gender and L1-ACH (an L1 × L1 latent interaction) are not significant. Although random-slope models show no significant school-to-school variation in relations between L1-ACH and L1-ASC, the negative effects of L2-ACH (the BFLPE) do vary somewhat with individual L1-ACH.

We conclude with implications for diverse applications of the set of latent contextual models, including recommendations about their implementation, effect size estimates (and confidence intervals) appropriate to multilevel models, and directions for further research in contextual effect analysis.     

Multilevel factor analysis and structural equation modeling of daily diary coping data: Modeling trait and state variation

The current study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data was collected on a large (n = 366) multiethnic sample over the course of five days. Intraclass correlation coefficient for the derived factors suggested approximately equal amounts of variability in coping usage at the state and trait levels. MFAs showed that Problem-Focused Coping and Social Support emerged as stable factors at both the within-person and between-person levels. Other factors (Minimization, Emotional Rumination, Avoidance, Distraction) were specific to the within-person or between-person levels, but not both. Multilevel structural equation modeling (MSEM) showed that the prediction of daily positive and negative affect differed as a function of outcome and level of coping factor. The Discussion section focuses primarily on a conceptual and methodological understanding of modeling state and trait coping using daily diary data with MFA and MSEM to examine covariation among coping variables and predicting outcomes of interest.     

Multilevel modeling: overview and applications to research in counseling psychology

Multilevel modeling (MLM) is rapidly becoming the standard method of analyzing nested data, for example, data from students within multiple schools, data on multiple clients seen by a smaller number of therapists, and even longitudinal data. Although MLM analyses are likely to increase in frequency in counseling psychology research, many readers of counseling psychology journals have had only limited exposure to MLM concepts. This paper provides an overview of MLM that blends mathematical concepts with examples drawn from counseling psychology. This tutorial is intended to be a first step in learning about MLM; readers are referred to other sources for more advanced explorations of MLM. In addition to being a tutorial for understanding and perhaps even conducting MLM analyses, this paper reviews recent research in counseling psychology that has adopted a multilevel framework, and it provides ideas for MLM approaches to future research in counseling psychology.